Vacuum permittivity
Fundamental constant quantifying vacuum's response to electric fields.
Vacuum permittivity, written as ε₀ (said "epsilon nought" or "epsilon zero"), is the absolute dielectric permittivity of a classical vacuum. It is also called the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum, and it serves as an ideal baseline physical constant. This constant indicates how dense an electric field can become in the presence of electric charges, linking the unit for electric charge to mechanical units like length and force. For instance, Coulomb’s law uses ε₀ to describe the force between two spherically symmetric electric charges separated in a vacuum: F_C = (1/(4πε₀)) × (q₁q₂/r²). Here, q₁ and q₂ are the charges, r is the distance between their centers, and the factor 1/(4πε₀) is roughly 9×10⁹ N·m²·C⁻². The constant also appears in Maxwell’s equations, which govern electric and magnetic fields, electromagnetic radiation, and their sources. In electrical engineering, ε₀ is used as a unit to quantify the permittivity of dielectric materials.
The value of ε₀ follows from the formula ε₀ = 1/(μ₀c²), where c is the defined speed of light in a classical vacuum in SI units, and μ₀ is the magnetic constant (also called vacuum permeability or the permeability of free space). With μ₀ approximately 4π × 10⁻⁷ H/m (based on the former definition of the ampere) and c exactly 299,792,458 m/s, ε₀ works out to about 8.8541878176 × 10⁻¹² F/m. The relative deviation of the recommended measured value (0.13 parts per billion) from the former defined value falls within its uncertainty (0.16 parts per billion). The historical origins of ε₀ and its value are explained in more detail below.
With the revision of the SI on 20 May 2019, the elementary charge was redefined exactly in terms of the coulomb. As a result, the vacuum electric permittivity and magnetic vacuum permeability no longer have exactly determined values in SI units. The electron charge became a numerically defined quantity, making both ε₀ and μ₀ measured quantities—neither exact—but still related by the equation ε₀μ₀c² = 1. These values are determined by the experimentally measured fine-structure constant α.
- symbol
- ε0 (epsilon nought or epsilon zero)
- CODATA value
- 8.8541878176 × 10⁻¹² F/m
- also known as
- permittivity of free space, electric constant, distributed capacitance of the vacuum
- relation
- ε0 = 1/(μ0c²)
- relative uncertainty
- 1.6 × 10⁻¹⁰ (as of 2019 SI revision)
Lore & Background
The parameter ε0 has historically been known by many names, including vacuum permittivity, permittivity of free space, and electric constant. Its presence in electromagnetic equations results from the rationalization process of units. The experiments of Coulomb and others showed that the force between two point-like amounts of electricity in free space follows a formula involving a constant ke, which relates to ε0.
ε0 appears in Coulomb's law, where the force between two separated electric charges is given by FC = 1/(4πε0) × q1q2/r², with 1/(4πε0) approximately 9×10⁹ N·m²·C⁻². It also appears in Maxwell's equations, describing properties of electric and magnetic fields and electromagnetic radiation.
The value of ε0 obeys the formula ε0 = 1/(μ0c²), where c is the defined speed of light and μ0 is the magnetic constant. Before the 2019 SI revision, ε0 had an exact defined value; after the redefinition of the elementary charge, ε0 became a measured quantity with uncertainty tied to the fine-structure constant.
Reader's Guide
Vacuum permittivity is a cornerstone of classical electromagnetism, appearing in fundamental equations that describe electric fields, magnetic fields, and electromagnetic radiation. Its value relates the units for electric charge to mechanical quantities such as length and force. In electrical engineering, ε0 itself is used as a unit to quantify the permittivity of various dielectric materials. The constant's historical significance lies in its role in rationalizing electromagnetic units and in Maxwell's prediction that electromagnetic waves travel at the speed of light. The 2019 revision of the SI made ε0 a measured quantity rather than an exact defined constant, with its uncertainty now tied to the fine-structure constant. Despite this change, ε0 remains essential for understanding how electric fields form in response to charges and for linking mechanical and electrical measurements.
Did You Know?
- The CODATA value of vacuum permittivity is approximately 8.8541878176 × 10⁻¹² F/m.
- Vacuum permittivity appears in Coulomb's law as part of the constant 1/(4πε0), which is about 9×10⁹ N·m²·C⁻².
- After the 2019 SI revision, ε0 and μ0 became measured quantities with relative uncertainty of 1.6×10⁻¹⁰, tied to the fine-structure constant.
- The term 'dielectric constant of vacuum' for ε0 is considered obsolete by most modern authors.
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